Chancellor Angela Merkel of Germany has sued for peace with the European Central Bank (ECB), following weeks of feuding over how to rescue Greece from the devastating debt crisis threatening the future of the euro single currency.

Merkel announced on Friday that the decisions on a new three-year bailout package for Greece, tipped to run to €120bn (£106bn), would need to be agreed with the ECB.

At a Berlin summit with the French president, Nicolas Sarkozy, Merkel softened her terms for the Greek bailout, urged a quick decision, stressed that any participation by private creditors in the rescue should be voluntary, and insisted that a new package with Greece would be agreed together with the ECB.

Her climbdown was welcomed by the financial markets, as the prospect of Greece suffering a catastrophic disorderly default receded. The euro rallied strongly, gaining more than one cent against the dollar. Europe's major stock markets also closed higher as traders took a more positive view of the Greek situation.

The German media, though, promptly predicted that Merkel's olive branch could cost her politically at home.

"For the German government, this is a remarkable shift," said the liberal Sueddeutsche Zeitung. "The chancellor has backed off from a central German demand," said the conservative Frankfurter Allgemeine Zeitung.

In a research note, JP Morgan said that Berlin seemed to be dropping its insistence on a bond swap by Greece's private creditors, the central factor that the ECB feared would cause the country to be declared in sovereign default.

The Berlin summit came at the end of a week of intense political and market turbulence, with riots on the streets of Athens, a Greek government on the brink of collapse, and bad-tempered disarray among EU leaders. And despite the apparent progress, it remains to be seen how the second Greek bailout in a year will be structured.

Sarkozy has been on the ECB side of the argument, and characteristically he claimed a breakthrough in Berlin, saying that France and Germany were united on all the essential points on Greece.

Merkel has become increasingly isolated in the last fortnight over Germany's insistence that Greece's private creditors – the banks, pension funds and insurance companies holding much of the insolvent country's €340bn of debt – have to take "haircuts" or sizeable losses on their investments as part of this second deal to rescue Greece.

The Germans wanted the creditors to swap maturing Greek bonds for new seven-year paper bonds on a scale that would be "quantifiable and substantial."

The ECB, supported by the European Commission, France and Jean-Claude Juncker of Luxembourg, head of the group of 17 eurozone countries, had warned that Berlin's policy could trigger calamity. The ratings agencies would declare Greece in default, bringing down the Greek banks and unleashing financial failure across the European banking sector.

The ECB recommended a rollover of Greek debt, with the banks pledging to buy new Greek paper as current loans are repaid, avoiding a "credit event" or a Greek default. It now seems that this option will prevail, and a deal will be reached much more quickly following Merkel's concessions.

She emphasised that any involvement by private creditors would be "explicitly voluntary".

A German parliament resolution last week underpinning her negotiating mandate in the EU stipulated that the German government could only agree to a new bailout "if an appropriate involvement of private creditors is included".

The Germans hoped this latter would amount to one quarter of the slated €120bn, but the contribution could now be merely symbolic. As she has consistently done throughout the 18-month crisis, Merkel had been playing for time, initially hoping to put off a new bailout until September. After the summit in Berlin, she said: "It's not about September. It's about the quickest possible solution."

Finance ministers from the eurozone and the EU meet in Luxembourg on Sunday and on Monday, and could now hammer out a bailout deal to be blessed by a European summit on Thursday.

Greece became the first eurozone country to require a bailout in May last year when the Europeans put together a €110bn package. That has failed amid escalating turmoil in Greece and growing resistance to the swingeing austerity programmes that were the price for the rescue.In a move offering further potential turmoil for the financial markets, the credit ratings agency Moody's said that it may cut Italy's sovereign credit rating from AA2, citing challenges ahead for economic growth due to structural weaknesses and a likely rise in interest rates. visit Luxembourg on Monday for talks with EU leaders who are anxious that the entire rescue scenario could still unravel because of his inability to deliver on a radical privatisation programme, spending cuts, and tax increases.

Merkel's remarks came as the IMF warned that debt-ridden European countries were "playing with fire" unless they took immediate steps to reduce their budget deficits.

The IMF, in its regular assessment of global economic prospects, said bigger threats to growth had emerged since its previous report in April, citing the eurozone debt crisis and signs of overheating in emerging market economies.

The IMF also revised downwards its forecast for US growth, estimating GDP would grow a tepid 2.5% this year and 2.7% in 2012 compared with an expected 2.8% and 2.9% growth, respectively, two months ago.